Nuprl Lemma : bor-btrue
∀[b:𝔹]. (b ∨btt ~ tt)
Proof
Definitions occuring in Statement :
bor: p ∨bq,
btrue: tt,
bool: 𝔹,
uall: ∀[x:A]. B[x],
sqequal: s ~ t
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uimplies: b supposing a,
squash: ↓T,
prop: ℙ,
true: True,
subtype_rel: A ⊆r B,
guard: {T},
iff: P ⇐⇒ Q,
and: P ∧ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
sq_type: SQType(T),
all: ∀x:A. B[x]
Lemmas referenced :
subtype_base_sq,
bool_wf,
bool_subtype_base,
equal_wf,
squash_wf,
true_wf,
bor_tt_simp,
btrue_wf,
iff_weakening_equal
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
thin,
instantiate,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
cumulativity,
hypothesis,
independent_isectElimination,
applyEquality,
lambdaEquality,
imageElimination,
hypothesisEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
natural_numberEquality,
sqequalRule,
imageMemberEquality,
baseClosed,
productElimination,
independent_functionElimination,
because_Cache,
dependent_functionElimination,
sqequalAxiom
Latex:
\mforall{}[b:\mBbbB{}]. (b \mvee{}\msubb{}tt \msim{} tt)
Date html generated:
2017_04_14-AM-07_30_38
Last ObjectModification:
2017_02_27-PM-02_59_17
Theory : bool_1
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