Nuprl Lemma : dl-sem-eq_wf
∀[a,b:Prog]. (a ≡ b ∈ ℙ')
Proof
Definitions occuring in Statement :
dl-sem-eq: a ≡ b,
dl-prog: Prog,
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
dl-sem-eq: a ≡ b,
prop: ℙ,
all: ∀x:A. B[x],
so_lambda: λ2x.t[x],
so_apply: x[s],
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
implies: P ⇒ Q,
and: P ∧ Q
Lemmas referenced :
nat_wf,
iff_wf,
dl-prog-sem_wf,
istype-nat,
dl-prog_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
functionEquality,
universeEquality,
cumulativity,
extract_by_obid,
hypothesis,
hypothesisEquality,
sqequalHypSubstitution,
isectElimination,
thin,
applyEquality,
lambdaEquality_alt,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
inhabitedIsType,
isect_memberEquality_alt,
isectIsTypeImplies,
universeIsType
Latex:
\mforall{}[a,b:Prog]. (a \mequiv{} b \mmember{} \mBbbP{}')
Date html generated:
2019_10_15-AM-11_45_51
Last ObjectModification:
2019_03_26-PM-00_04_10
Theory : dynamic!logic
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