Nuprl Lemma : mon_when_false
∀[g:GrpSig]. ∀[b:𝔹]. ∀[x:|g|]. (when b. x) = e ∈ |g| supposing ¬↑b
Proof
Definitions occuring in Statement :
mon_when: when b. p,
grp_id: e,
grp_car: |g|,
grp_sig: GrpSig,
assert: ↑b,
bool: 𝔹,
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
not: ¬A,
equal: s = t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
mon_when: when b. p,
all: ∀x:A. B[x],
implies: P ⇒ Q,
bool: 𝔹,
unit: Unit,
it: ⋅,
btrue: tt,
uiff: uiff(P;Q),
and: P ∧ Q,
ifthenelse: if b then t else f fi ,
not: ¬A,
false: False,
bfalse: ff,
prop: ℙ
Lemmas referenced :
bool_wf,
eqtt_to_assert,
uiff_transitivity,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqff_to_assert,
assert_of_bnot,
grp_id_wf,
equal_wf,
grp_car_wf,
grp_sig_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
hypothesisEquality,
thin,
extract_by_obid,
hypothesis,
lambdaFormation,
sqequalHypSubstitution,
unionElimination,
equalityElimination,
isectElimination,
because_Cache,
productElimination,
independent_isectElimination,
sqequalRule,
independent_functionElimination,
voidElimination,
baseClosed,
equalityTransitivity,
equalitySymmetry,
dependent_functionElimination,
isect_memberEquality,
axiomEquality
Latex:
\mforall{}[g:GrpSig]. \mforall{}[b:\mBbbB{}]. \mforall{}[x:|g|]. (when b. x) = e supposing \mneg{}\muparrow{}b
Date html generated:
2017_10_01-AM-08_17_05
Last ObjectModification:
2017_02_28-PM-02_01_54
Theory : groups_1
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