Nuprl Lemma : bor_mon_wf
<𝔹,∨b> ∈ AbMon
Proof
Definitions occuring in Statement :
bor_mon: <𝔹,∨b>,
abmonoid: AbMon,
member: t ∈ T
Definitions unfolded in proof :
bor_mon: <𝔹,∨b>,
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
assoc: Assoc(T;op),
infix_ap: x f y,
top: Top,
ident: Ident(T;op;id),
bor: p ∨bq,
ifthenelse: if b then t else f fi ,
bfalse: ff,
and: P ∧ Q,
cand: A c∧ B,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
comm: Comm(T;op),
all: ∀x:A. B[x],
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
exists: ∃x:A. B[x],
or: P ∨ Q,
sq_type: SQType(T),
bnot: ¬bb,
assert: ↑b,
false: False
Lemmas referenced :
mk_abmonoid,
bool_wf,
eq_bool_wf,
btrue_wf,
bor_wf,
bfalse_wf,
bor-assoc,
equal_wf,
squash_wf,
true_wf,
bor_ff_simp,
iff_weakening_equal,
eqtt_to_assert,
testxxx_lemma,
bor_tt_simp,
eqff_to_assert,
bool_cases_sqequal,
subtype_base_sq,
bool_subtype_base,
assert-bnot
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesis,
lambdaEquality,
hypothesisEquality,
independent_isectElimination,
isect_memberFormation,
sqequalRule,
isect_memberEquality,
voidElimination,
voidEquality,
axiomEquality,
because_Cache,
applyEquality,
imageElimination,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
independent_pairFormation,
independent_pairEquality,
lambdaFormation,
unionElimination,
equalityElimination,
dependent_functionElimination,
dependent_pairFormation,
promote_hyp,
instantiate,
cumulativity
Latex:
<\mBbbB{},\mvee{}\msubb{}> \mmember{} AbMon
Date html generated:
2017_10_01-AM-08_16_47
Last ObjectModification:
2017_02_28-PM-02_01_49
Theory : groups_1
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