Nuprl Lemma : es-interval-induction
∀es:EO. ∀i:Id.
∀[P:e1:{e:E| loc(e) = i ∈ Id} ⟶ {e2:E| loc(e2) = i ∈ Id} ⟶ ℙ]
(∀e1@i.∀e2≥e1.(∀e:E. ((e1 <loc e) ⇒ e ≤loc e2 ⇒ P[e;e2])) ⇒ P[e1;e2] ⇒ ∀e1@i.∀e2≥e1.P[e1;e2])
Proof
Definitions occuring in Statement :
alle-ge: ∀e'≥e.P[e'],
alle-at: ∀e@i.P[e],
es-le: e ≤loc e' ,
es-locl: (e <loc e'),
es-loc: loc(e),
es-E: E,
event_ordering: EO,
Id: Id,
uall: ∀[x:A]. B[x],
prop: ℙ,
so_apply: x[s1;s2],
all: ∀x:A. B[x],
implies: P ⇒ Q,
set: {x:A| B[x]} ,
function: x:A ⟶ B[x],
equal: s = t ∈ T
Definitions unfolded in proof :
all: ∀x:A. B[x],
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
alle-ge: ∀e'≥e.P[e'],
so_lambda: λ2x.t[x],
so_apply: x[s1;s2],
es-locl: (e <loc e'),
and: P ∧ Q,
uimplies: b supposing a,
subtype_rel: A ⊆r B,
so_apply: x[s],
nat: ℕ,
cand: A c∧ B,
iff: P ⇐⇒ Q,
rev_implies: P ⇐ Q,
ge: i ≥ j ,
decidable: Dec(P),
or: P ∨ Q,
le: A ≤ B,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
uiff: uiff(P;Q),
alle-at: ∀e@i.P[e],
less_than: a < b,
squash: ↓T
Latex:
\mforall{}es:EO. \mforall{}i:Id.
\mforall{}[P:e1:\{e:E| loc(e) = i\} {}\mrightarrow{} \{e2:E| loc(e2) = i\} {}\mrightarrow{} \mBbbP{}]
(\mforall{}e1@i.\mforall{}e2\mgeq{}e1.(\mforall{}e:E. ((e1 <loc e) {}\mRightarrow{} e \mleq{}loc e2 {}\mRightarrow{} P[e;e2])) {}\mRightarrow{} P[e1;e2]
{}\mRightarrow{} \mforall{}e1@i.\mforall{}e2\mgeq{}e1.P[e1;e2])
Date html generated:
2016_05_16-AM-09_51_22
Last ObjectModification:
2016_01_17-PM-01_28_13
Theory : new!event-ordering
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