Nuprl Lemma : pscm-ap-type-at
∀[B,s,x,K:Top]. ((B)s(x) ~ B((s)x))
Proof
Definitions occuring in Statement :
pscm-ap-type: (AF)s,
presheaf-type-at: A(a),
pscm-ap: (s)x,
uall: ∀[x:A]. B[x],
top: Top,
sqequal: s ~ t
Definitions unfolded in proof :
presheaf-type-at: A(a),
pi1: fst(t),
uall: ∀[x:A]. B[x],
so_lambda: so_lambda(x,y,z,w.t[x; y; z; w]),
member: t ∈ T,
so_apply: x[s1;s2;s3;s4],
top: Top,
uimplies: b supposing a,
strict4: strict4(F),
and: P ∧ Q,
all: ∀x:A. B[x],
implies: P ⇒ Q,
has-value: (a)↓,
prop: ℙ,
guard: {T},
or: P ∨ Q,
squash: ↓T,
so_lambda: λ2x y.t[x; y],
so_apply: x[s1;s2],
pscm-ap-type: (AF)s,
pscm-ap: (s)x
Lemmas referenced :
lifting-strict-spread,
has-value_wf_base,
base_wf,
is-exception_wf,
strict4-spread,
top_wf
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
cut,
introduction,
extract_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
baseClosed,
isect_memberEquality,
voidElimination,
voidEquality,
independent_isectElimination,
independent_pairFormation,
lambdaFormation,
callbyvalueApply,
hypothesis,
baseApply,
closedConclusion,
hypothesisEquality,
applyExceptionCases,
inrFormation,
imageMemberEquality,
imageElimination,
inlFormation,
instantiate,
because_Cache,
isect_memberFormation,
sqequalAxiom
Latex:
\mforall{}[B,s,x,K:Top]. ((B)s(x) \msim{} B((s)x))
Date html generated:
2018_05_22-PM-10_03_26
Last ObjectModification:
2018_05_20-PM-09_47_42
Theory : presheaf!models!of!type!theory
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