Nuprl Lemma : fpf-rename-cap
∀[A,C,B:Type]. ∀[eqa:EqDecider(A)]. ∀[eqc:EqDecider(C)]. ∀[r:A ─→ C]. ∀[f:a:A fp-> B]. ∀[a:A]. ∀[z:B].
rename(r;f)(r a)?z = f(a)?z ∈ B supposing Inj(A;C;r)
Proof
Definitions occuring in Statement :
fpf-rename: rename(r;f),
fpf-cap: f(x)?z,
fpf: a:A fp-> B[a],
deq: EqDecider(T),
inject: Inj(A;B;f),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
apply: f a,
function: x:A ─→ B[x],
universe: Type,
equal: s = t ∈ T
Lemmas :
bool_wf,
fpf-dom_wf,
subtype-fpf2,
top_wf,
fpf-rename-ap,
equal-wf-T-base,
assert_wf,
bnot_wf,
not_wf,
eqtt_to_assert,
uiff_transitivity,
eqff_to_assert,
assert_of_bnot,
inject_wf,
fpf_wf,
deq_wf,
fpf-rename_wf,
fpf-rename-dom
\mforall{}[A,C,B:Type]. \mforall{}[eqa:EqDecider(A)]. \mforall{}[eqc:EqDecider(C)]. \mforall{}[r:A {}\mrightarrow{} C]. \mforall{}[f:a:A fp-> B]. \mforall{}[a:A].
\mforall{}[z:B].
rename(r;f)(r a)?z = f(a)?z supposing Inj(A;C;r)
Date html generated:
2015_07_17-AM-11_11_02
Last ObjectModification:
2015_01_28-AM-07_44_20
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